sin^2(pie*Z) is sin[tex]^{2}[/tex]([tex]\pi[/tex]z)?
If it is, Then can't you use the chain rule? which is power rule on the whole out side of the ( ) and then it by multiply by the derivatives of the inside of the ( ). because sin[tex]^{2}[/tex]([tex]\pi[/tex]z) is just the same as (sin([tex]\pi[/tex]z))[tex]^{2}[/tex]

hm..I believe the derivative of sin is cos. so the answer should be 2cos(pi*Z) * (Pi) or 2[tex]\pi[/tex]cos([tex]\pi[/tex]Z).

the first part is power rule and derivative of the Sin which is Cos. for the inside of the ( ), since it's product of a variable and a constant, we know that Pi is a number hence it a constant. So you take the dervitive of pi*Z and use the product rule:
it will be
Pi*1 + Z*(0)=Pi.

hm..I believe the derivative of sin is cos. so the answer should be 2cos(pi*Z) * (Pi) or 2[tex]\pi[/tex]cos([tex]\pi[/tex]Z).

the first part is power rule and derivative of the Sin which is Cos. for the inside of the ( ), since it's product of a variable and a constant, we know that Pi is a number hence it a constant. So you take the dervitive of pi*Z and use the product rule:
it will be
Pi*1 + Z*(0)=Pi.

NO product rule! [itex]\pi[/itex] is NOT a variable, it is a constant just like 2 or [itex]\frac{3}{4}[/itex] or any other NUMBER.

The chain rule qualitatively says: Take the derivative of the 'outside function' with the inside function as its argument and multiply it times the derivative of the 'inside function'.

In this case there are 2 outside functions. Start with the squared function and work your way inwards.